{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Thermal Expansion\n",
    "# 1. Introduction\n",
    "- A given crystal should have a well defined average lattice constant at a given pressure and temperature. Here we use silicon as an example to show how to calculate lattice constants using <code>GPUMD</code>. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing Relevant Functions\n",
    "- The inputs/outputs for GPUMD are processed using the [Atomic Simulation Environment (ASE)](https://wiki.fysik.dtu.dk/ase/) and the [thermo](https://github.com/AlexGabourie/thermo) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import *\n",
    "from ase.lattice.cubic import Diamond\n",
    "from thermo.gpumd.io import ase_atoms_to_gpumd\n",
    "from thermo.gpumd.data import load_thermo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Preparing the Inputs\n",
    "- We use a cubic system (of diamond structure) consisting of $10^3\\times 8 = 8000$ silicon atoms and use the minimal Tersoff potential [[Fan 2020]](https://doi.org/10.1088/1361-648X/ab5c5f).\n",
    "\n",
    "## Generate the  [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lattice(symbols='Si8000', pbc=True, cell=[54.3, 54.3, 54.3])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Si = Diamond('Si', size=(10,10,10))\n",
    "Si"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ase_atoms_to_gpumd(Si, M=4, cutoff=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The first few lines of the [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file are:\n",
    "```\n",
    "8000 4 3 0 0 0\n",
    "1 1 1 54.3 54.3 54.3\n",
    "0 0 0 0 28\n",
    "0 0 2.715 2.715 28\n",
    "0 2.715 0 2.715 28\n",
    "0 2.715 2.715 0 28\n",
    "```\n",
    "- Explanations for the first line:\n",
    " - The first number states that the number of particles is 8000. \n",
    " - The second number in this line, 4, is good for silicon crystals described by the Tersoff potential because no atom can have more than 4 neighbor atoms in the temperature range studied. Making this number larger only results in more memory usage. If this number is not large enough, <code>GPUMD</code> will give an error message and exit.\n",
    " - The next number, 3, means the initial cutoff distance for the neighbor list construction is 3 A. Here, we only need to consider the first nearest neighbors. Any number larger than the first nearest neighbor distance and smaller than the second nearest neighbor distance is OK here. Note that we will also not update the neighbor list. There is no such need in this problem. \n",
    " - The remaining three zeros in the first line mean: \n",
    "   - the box is orthogonal;\n",
    "   - the initial velocities are not contained in this file; \n",
    "   - there is no grouping method defined here. \n",
    " \n",
    "- Explanations for the second line:\n",
    " - The first three 1's mean that all three directions are periodic. \n",
    " - The remaining three numbers are the box lengths in the three directions. It can be seen that we have used an initial lattice constant of 5.43 A to build the model.\n",
    "\n",
    "- Starting from the third line, the numbers in the first column are all 0 here, which means that all the atoms are of type 0 (single atom-type system). The next three columns are the initial coordinates of the atoms. The last column gives the masses of the atoms. Here, we show isotopically pure Si-28 crystal, but this Jupyter notebook will generate an [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file using the average of the various isotopes of Si. In some applications, one can consider mass disorder in a flexible way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The <code>run.in</code> file:\n",
    "The <code>run.in</code> input file is given below:<br>\n",
    "```\n",
    "potential   potentials/tersoff/Si_Fan_2019.txt 0\n",
    "velocity    100\n",
    "\n",
    "ensemble    npt_ber 100 100 0.01 0 0 0 0.0005\n",
    "time_step   1\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 200 200 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 300 300 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 400 400 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 500 500 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 600 600 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 700 700 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 800 800 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 900 900 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "\n",
    "ensemble    npt_ber 1000 1000 0.01 0 0 0 0.0005\n",
    "dump_thermo 10\n",
    "run         20000\n",
    "```\n",
    "- The first line uses the [potential](https://gpumd.zheyongfan.org/index.php/The_potential_keyword) keyword to define the potential to be used, which is specified in the file [Si_Fan_2019.txt](https://github.com/brucefan1983/GPUMD/blob/master/potentials/tersoff/Si_Fan_2019.txt).\n",
    "\n",
    "- The second line uses the [velocity](https://gpumd.zheyongfan.org/index.php/The_velocity_keyword) keyword and sets the velocities to be initialized with a temperature of 100 K. \n",
    "\n",
    "- The following 4 lines define the first [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword). This [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) will be in the NPT [ensemble](https://gpumd.zheyongfan.org/index.php/The_ensemble_keyword), using the Berendsen method. The temperature is 100 K and the pressures are zero in all the directions. The coupling constants are 0.01 (dimensionless) and 0.0005 (in the natural unit system adopted by GPUMD) for the thermostat and the barostat, respectively. The [time_step](https://gpumd.zheyongfan.org/index.php/The_time_step_keyword) for integration is 1 fs. There are $2\\times 10^4$ steps for this [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) and the thermodynamic quantities will be output every 10 steps. \n",
    "\n",
    "- After this run, there are 9 other runs with the same parameters but different target temperatures. Note that the time step only needs to be set once if one wants to use the same time step in the whole simulation. In contrast, one has to use the [dump_thermo](https://gpumd.zheyongfan.org/index.php/The_dump_thermo_keyword) keyword for each run in order to get outputs for each run. That is, we can say that the [time_step](https://gpumd.zheyongfan.org/index.php/The_time_step_keyword) keyword is propagating and the [dump_thermo](https://gpumd.zheyongfan.org/index.php/The_dump_thermo_keyword) keyword is non-propagating."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Results and Discussion\n",
    "- It takes less than 1 min to run this example when a Tesla K40 card is used. The speed of the run is about $3\\times 10^7$ atom x step / second. Using a Tesla P100, the speed is close to $10^8$ atom x step / second."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure Properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "aw = 2\n",
    "fs = 16\n",
    "font = {'size'   : fs}\n",
    "matplotlib.rc('font', **font)\n",
    "matplotlib.rc('axes' , linewidth=aw)\n",
    "\n",
    "def set_fig_properties(ax_list):\n",
    "    tl = 8\n",
    "    tw = 2\n",
    "    tlm = 4\n",
    "    \n",
    "    for ax in ax_list:\n",
    "        ax.tick_params(which='major', length=tl, width=tw)\n",
    "        ax.tick_params(which='minor', length=tlm, width=tw)\n",
    "        ax.tick_params(which='both', axis='both', direction='in', right=True, top=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Thermal Expansion\n",
    "- The output file [thermo.out](https://gpumd.zheyongfan.org/index.php/The_thermo.out_output_file) contains many useful data. Here, we load the results and plot the data in the following figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['T', 'K', 'U', 'Px', 'Py', 'Pz', 'Lx', 'Ly', 'Lz'])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thermo = load_thermo()\n",
    "thermo.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 0.01*np.arange(1,thermo['T'].shape[0]+1) # [ps]\n",
    "NC = 10  # Number of cells in each direction\n",
    "NT = 10  # Number of temperature steps\n",
    "temp = np.arange(100,1001,100)\n",
    "M = thermo['T'].shape[0]//NT\n",
    "a = (thermo['Lx']+thermo['Ly']+thermo['Lz'])/(3*NC)\n",
    "Pave = (thermo['Px']+thermo['Py']+thermo['Pz'])/3.\n",
    "a_ave = a.reshape(NT, M)[:,M//2+1:].mean(axis=1)\n",
    "fit = np.poly1d(np.polyfit(temp, a_ave, deg=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(12,10))\n",
    "subplot(2,2,1)\n",
    "set_fig_properties([gca()])\n",
    "plot(t, thermo['T'])\n",
    "xlim([0, 200])\n",
    "gca().set_xticks(range(0,201,50))\n",
    "ylim([0, 1100])\n",
    "gca().set_yticks(range(0,1101,500))\n",
    "ylabel('Temperature (K)')\n",
    "xlabel('Time (ps)')\n",
    "title('(a)')\n",
    "\n",
    "subplot(2,2,2)\n",
    "set_fig_properties([gca()])\n",
    "plot(t, Pave)\n",
    "xlim([0, 200])\n",
    "gca().set_xticks(range(0,201,50))\n",
    "ylim([-0.1, 0.4])\n",
    "gca().set_yticks(np.arange(-1,5)/10)\n",
    "ylabel('Pressure (GPa)')\n",
    "xlabel('Time (ps)')\n",
    "title('(b)')\n",
    "\n",
    "subplot(2,2,3)\n",
    "set_fig_properties([gca()])\n",
    "plot(t, a,linewidth=3)\n",
    "xlim([0, 200])\n",
    "gca().set_xticks(range(0,201,50))\n",
    "ylim([5.43, 5.48])\n",
    "gca().set_yticks([5.44,5.46,5.48])\n",
    "ylabel(r'a ($\\AA$)')\n",
    "xlabel('Time (ps)')\n",
    "title('(c)')\n",
    "\n",
    "subplot(2,2,4)\n",
    "set_fig_properties([gca()])\n",
    "Tpoly = [0, 1100]\n",
    "plot(Tpoly, fit(Tpoly),color='C3')\n",
    "scatter(temp, a_ave,s=200,zorder=100,facecolor='none',edgecolors='C0',linewidths=3)\n",
    "xlim([0, 1100])\n",
    "gca().set_xticks(range(0,1101,500))\n",
    "ylim([5.43, 5.48])\n",
    "gca().set_yticks([5.44,5.46,5.48])\n",
    "ylabel(r'a ($\\AA$)')\n",
    "xlabel('Temperature (K)')\n",
    "title('(d)')\n",
    "\n",
    "tight_layout()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(a)** Instant temperature as a function of simulation time. **(b)** Instant pressure as a function of simulation time. **(c)** Instant lattice constant as a function of simulation time. **(d)** Averaged lattice constant (over the last 10 ps in each run for a given temperature) as a function of temperature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additional figure notes:<br>\n",
    "- (a): The temperature for each run quickly reaches the target temperature (with fluctuations).\n",
    "\n",
    "- (b): The pressure (averaged over the three directions) for each run quickly reaches the target pressure zero (with fluctuations).\n",
    "\n",
    "- (c): The lattice constant (averaged over the three directions) for each run reaches a plateau (with fluctuations) after some steps.\n",
    "\n",
    "- (d): We calculate the average lattice constant at each temperature by averaging the second half of the data for each run. The average lattice constants at different temperatures can be well fit by a linear function, with the thermal expansion coefficient being estimated to be $\\alpha \\approx 7.2 \\times 10^{-6} $ K<sup>-1</sup>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. References\n",
    "[Fan 2020] Zheyong Fan, Yanzhou Wang, Xiaokun Gu, Ping Qian, Yanjing Su, and Tapio Ala-Nissila, [A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties](https://doi.org/10.1088/1361-648X/ab5c5f), J. Phys.: Condens. Matter **32** 135901 (2020)."
   ]
  }
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